Localization of the discontinuity line of the right-hand side of a differential equation

D. S. Konovalova

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Localization of the discontinuity line of the right-hand side of a differential equation

机译：微分方程右侧不连续线的局部化

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摘要

We propose a new approach to studying the inverse problems for differential equations with constant coefficients. Its application is illustrated by an example of some partial differential equation with three independent variables. The right-hand side of the equation is assumed to be a function discontinuous in spatial variables. In the inverse problem, it is required to find some hull containing the discontinuity line of the right-hand side. An algorithm for constructing such a hull is obtained: It is a square whose sides are tangent to the discontinuity line.

机译：我们提出了一种新的方法来研究常系数微分方程的反问题。一个带有三个独立变量的偏微分方程的例子说明了它的应用。假设等式的右侧是空间变量中不连续的函数。在反问题中，需要找到一些包含右侧不连续线的船体。得到一种构造这种船体的算法：它是一个正方形，其边与不连续线相切。

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来源
《Journal of applied and industrial mathematics》 |2016年第1期|共9页
作者
D. S. Konovalova;
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正文语种 eng
中图分类应用数学;
关键词
inverse problem; discontinuous function; weak solution; differential properties;

机译：反问题;间断函数;弱解;微分性质;

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专利

1. Localization of the discontinuity line of the right-hand side of a differential equation [J] . D. S. Konovalova Journal of applied and industrial mathematics . 2016,第1期

机译：微分方程右侧不连续线的局部化
2. The Maslov canonical operator on a pair of Lagrangian manifolds and asymptotic solutions of stationary equations with localized right-hand sides [J] . Anikin A. Yu., Dobrokhotov S. Yu., Nazaikinskii V. E., Doklady. Mathematics . 2017,第1期

机译：Maslov规范操作员在一对拉格朗日歧管和局部右侧固定式方程的渐近解
3. Dynamic Right-Hand Side Reconstruction Problem for a System of Fractional Differential Equations [J] . Surkov P. G. Differential equations: A translation of differensial'nye uraveniya . 2019,第6期

机译：分数微分方程系统动态右侧重建问题
4. Optimal Estimation of Unknown Right-Hand Sides of First Order Linear Systems of Periodic Ordinary Differential Equations from Indirect Noisy Observations of Their Solutions [C] . Oleksandr Nakonechnyi, Yuri Podlipenko IEEE International Conference on System Analysis and Intelligent Computing . 2020

机译：从其解的间接噪声观测值估计一阶常微分方程线性系统的未知右手边的最优估计
5. High-accuracy numerical methods for ordinary differential equations with discontinuous right-hand side [D] . Stewart, David Edward 1990

机译：右手不连续的常微分方程的高精度数值方法
6. Gaussian Process Regression for Data Fulfilling Linear Differential Equations with Localized Sources [O] . Christopher G. Albert, Katharina Rath 2020

机译：高斯进程回归数据满足局部源的线性微分方程
7. The Maslov canonical operator on a pair of Lagrangian manifolds and asymptotic solutions of stationary equations with localized right-hand sides [O] . Anikin, A. Yu., Dobrokhotov, S. Yu., Nazaikinskii, V. E., 2017

机译：一对拉格朗日流形上的Maslov正则算子和具有局部右手边的平稳方程的渐近解

Localization of the discontinuity line of the right-hand side of a differential equation

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